# Thread: I'm stuck with simple DE

1. ## I'm stuck with simple DE

Hi!
Could someone please help me. I don't know how to solve this DE and I have exams coming up tomorrow....

(xy )d/dx = (y^2)*(x^1/2) , with the condition y(1) = 1.

I would be most grateful for any help.

Best regards,
Sara
[IMG]file:///C:/DOCUME%7E1/SARASE%7E1/LOCALS%7E1/Temp/moz-screenshot-2.png[/IMG]

2. Do you mean $xy\dot{y}=y^2\sqrt{x}$?

If so, it is seperable to ${\mathrm{d}y\over y} = {\mathrm{d}x\over\sqrt{x}}$, which can be solved by integrating from 1 to x.

[Another method is to multiply by an integrating factor h and rearrange to get $h\sqrt{x}y\dot{y}-hy^2=0$, and then look for a function g s.t. the LHS is $=\frac{\mathrm{d}}{\mathrm{d}x}(gy^2) = \dot{g}y^2 + 2gy\dot{y}$ by equating coefficients of like terms, but this is probably harder so I'm not sure why I mentioned it........ ]

Anyway, check your formula, I think it might have a typo.

P.S. Images must be located by a URL, so for instance, the local path to an image on your personal machine will not do.